Lecture 7 Quantitative Process Analysis II

Transcription

1 MTAT Business Process Management Lecture 7 Quantitative Process Analysis II Marlon Dumas marlon.dumas ät ut. ee 1

2 Process Analysis 2

3 Process Analysis Techniques Qualitative analysis Value-Added & Waste Analysis Root-Cause Analysis Pareto Analysis Issue Register Quantitative Analysis Flow analysis Queuing analysis Simulation 3

4 1. Introduction 2. Process Identification 3. Essential Process Modeling 4. Advanced Process Modeling 5. Process Discovery 6. Qualitative Process Analysis 7. Quantitative Process Analysis 8. Process Redesign 9. Process Automation 10.Process Intelligence 4

5 Why flow analysis is not enough? Flow analysis does not consider waiting times due to resource contention Queuing analysis and simulation address these limitations and have a broader applicability 5

6 Queuing Analysis Capacity problems are common and a key driver of process redesign Need to balance the cost of increased capacity against the gains of increased productivity and service Queuing and waiting time analysis is particularly important in service systems Large costs of waiting and/or lost sales due to waiting Prototype Example ER at a Hospital Patients arrive by ambulance or by their own accord One doctor is always on duty More patients seeks help longer waiting times Question: Should another MD position be instated? Laguna & Marklund 6

7 Delay is Caused by Job Interference If arrivals are regular or sufficiently spaced apart, no queuing delay occurs Deterministic traffic Variable but spaced apart traffic Dimitri P. Bertsekas 7

8 Burstiness Causes Interference Queuing results from variability in processing times and/or interarrival intervals Dimitri P. Bertsekas 8

9 Job Size Variation Causes Interference Deterministic arrivals, variable job sizes Dimitri P. Bertsekas 9

10 High Utilization Exacerbates Interference The queuing probability increases as the load increases Utilization close to 100% is unsustainable too long queuing times Dimitri P. Bertsekas 10

11 The Poisson Process Common arrival assumption in many queuing and simulation models The times between arrivals are independent, identically distributed and exponential P (arrival < t) = 1 e -λt Key property: The fact that a certain event has not happened tells us nothing about how long it will take before it happens e.g., P(X > 40 X >= 30) = P (X > 10) Laguna & Marklund 11

12 Negative Exponential Distribution 12

13 Queuing theory: basic concepts arrivals waiting service c Basic characteristics: (mean arrival rate) = average number of arrivals per time unit (mean service rate) = average number of jobs that can be handled by one server per time unit: c = number of servers Wil van der Aalst 13

14 Queuing theory concepts (cont.) Wq,Lq c W,L Given, and c, we can calculate : = resource utilization Wq = average time a job spends in queue (i.e. waiting time) W = average time in the system (i.e. cycle time) Lq = average number of jobs in queue (i.e. length of queue) L = average number of jobs in system (i.e. Work-in- Progress) Wil van der Aalst 14

15 M/M/1 queue Assumptions: time between arrivals and processing time follow a negative exponential distribution 1 server (c = 1) FIFO L= /(1- ) W=L/ =1/( - ) 1 ρ = Capacity Demand Available Capacity = L q = 2 /(1- ) = L- λ μ Wq=Lq/ = /( ( - )) Laguna & Marklund 15

16 M/M/c queue Now there are c servers in parallel, so the expected capacity per time unit is then c* = Capacity Demand Available Capacity = c* Little s Formula Wq=Lq/ W=Wq+(1/ ) Little s Formula L= W Laguna & Marklund 16

17 Tool Support For M/M/c systems, the exact computation of Lq is rather complex P 0 L q = = n= c c 1 n= 0 (n c)p ( / ) n! n n =... = ( / ) c! ( / ) c c!(1 ) c 2 P ( /(c ) 1 Consider using a tool, e.g. (very simple) (more sophisticated, Excel add-on) 17

18 Example ER at County Hospital Situation Patients arrive according to a Poisson process with intensity ( the time between arrivals is exp( ) distributed. The service time (the doctor s examination and treatment time of a patient) follows an exponential distribution with mean 1/ (=exp( ) distributed) The ER can be modeled as an M/M/c system where c = the number of doctors Data gathering = 2 patients per hour = 3 patients per hour Question Should the capacity be increased from 1 to 2 doctors? Laguna & Marklund 18

19 Queuing Analysis Hospital Scenario Interpretation To be in the queue = to be in the waiting room To be in the system = to be in the ER (waiting or under treatment) Characteristic One doctor (c=1) Two Doctors (c=2) 2/3 1/3 Lq 4/3 patients 1/12 patients L 2 patients 3/4 patients Wq 2/3 h = 40 minutes 1/24 h = 2.5 minutes W 1 h 3/8 h = 22.5 minutes Is it warranted to hire a second doctor? Laguna & Marklund 19

20 Your turn Textbook, Chapter 7, exercise 7.12 We consider a Level-2 IT service desk with two staff members. Each staff member can handle one service request in 4 working hours on average. Service times are exponentially distributed. Requests arrive at a mean rate of one request every 3 hours according to a Poisson process. What is the average time between the moment a service request arrives at this desk and the moment it is fulfilled? Now consider the scenario where the number of requests becomes one per hour. How many level-2 staff are required to be able to start serving a request on average within two working hours of it being received? 20

21 Process Simulation Versatile quantitative analysis method for As-is analysis What-if analysis In a nutshell: Run a large number of process instances Gather performance data (cost, time, resource usage) Calculate statistics from the collected data 21

22 Process Simulation Model the process Define a simulation scenario Run the simulation Repeat for alternative scenarios Analyze the simulation outputs 22

23 Example 23

24 Example 24

25 Elements of a simulation scenario 1. Processing times of activities Fixed value Probability distribution 25

26 Exponential Distribution 26

27 Normal Distribution 27

28 Choice of probability distribution Fixed Rare, can be used to approximate case where the activity processing time varies very little Example: a task performed by a software application Normal Repetitive activities Example: Check completeness of an application Exponential Complex activities that may involve analysis or decisions Example: Assess an application 28

29 Simulation Example Normal(10m, 2m) Normal(10m, 2m) 0m Exp(20m) Normal(20m, 4m) Normal(10m, 2m) 29

30 Elements of a simulation model 1. Processing times of activities Fixed value Probability distribution 2. Conditional branching probabilities 3. Arrival rate of process instances and probability distribution Typically exponential distribution with a given mean inter-arrival time Arrival calendar, e.g. Monday-Friday, 9am-5pm, or 24/7 30

31 Branching probability and arrival rate Arrival rate = 2 applications per hour Inter-arrival time = 0.5 hour Negative exponential distribution From Monday-Friday, 9am-5pm m 55m 9:00 10:00 11:00 12:00 13:00 13:00 31

32 Elements of a simulation model 1. Processing times of activities Fixed value Probability distribution 2. Conditional branching probabilities 3. Arrival rate of process instances Typically exponential distribution with a given mean inter-arrival time Arrival calendar, e.g. Monday-Friday, 9am-5pm, or 24/7 4. Resource pools 32

33 Resource pools Name Size of the resource pool Cost per time unit of a resource in the pool Availability of the pool (working calendar) Examples Clerk 25 per hour Monday-Friday, 9am-5pm Credit Officer 25 per hour Monday-Friday, 9am-5pm In some tools, it is possible to define cost and calendar per resource, rather than for entire resource pool 33

34 Elements of a simulation model 1. Processing times of activities Fixed value Probability distribution 2. Conditional branching probabilities 3. Arrival rate of process instances and probability distribution Typically exponential distribution with a given mean inter-arrival time Arrival calendar, e.g. Monday-Friday, 9am-5pm, or 24/7 4. Resource pools 5. Assignment of tasks to resource pools 34

35 Resource pool assignment Clerk Officer Officer Syste m Clerk Officer 35

36 Process Simulation Model the process Define a simulation scenario Run the simulation Repeat for alternative scenarios Analyze the simulation outputs 36

37 Output: Performance measures & histograms 37

38 Process Simulation Model the process Define a simulation scenario Run the simulation Repeat for alternative scenarios Analyze the simulation outputs 38

39 Tools for Process Simulation ARIS ITP Commerce Process Modeler for Visio Logizian Oracle BPA Progress Savvion Process Modeler ProSim Bizagi Process Modeler Check tutorial at Signavio + BIMP 39

40 BIMP bimp.cs.ut.ee Accepts standard BPMN 2.0 as input Simple form-based interface to enter simulation scenario Produces KPIs + simulation logs in MXML format Simulation logs can be imported to the ProM process mining tool 40

41 BIMP Demo 41

42 Your turn Textbook, Chapter 7, exercise 7.8 (page 240) 42

43 Pitfalls of simulation Stochasticity Data quality Simplifying assumptions 43

44 Stochasticity Problem Simulation results may differ from one run to another Solutions 1. Make the simulation timeframe long enough to cover weekly and seasonal variability, where applicable 2. Use multiple simulation runs, average results of multiple runs, compute confidence intervals Multiple simulation runs Average results of multiple runs Compute confidence intervals 44

45 Data quality Problem Simulation results are only as trustworthy as the input data Solutions: 1. Rely as little as possible on guesstimates. Use input analysis where possible: Derive simulation scenario parameters from numbers in the scenario Use statistical tools to check fit the probability distributions 2. Simulate the as is scenario and cross-check results against actual observations 45

46 Simulation assumptions That the process model is always followed to the letter No deviations No workarounds That resources work constantly and non-stop Every day is the same! No tiredness effects No distractions beyond stochastic ones 46

47 Next week 47